SystemModeler in Education

Frida Svensson     Anna Palmer       Emil Arkstål

Patrik Ekenberg, Jan Brugård
Wolfram MatCore AB

Join the Conversation #WolframTechConf

Abstract

This talk will show how SystemModeler and the WolframLanguage can be used in highschool  and universities to explain concepts that would otherwise be very hard for the students to understand.

Examples from physics, life science, and chemistry will be given. The material, including teacher material and student assignments, will be made available for the participants.

Overview of Available Material

Primary and Highshools

Physics

Life Science

Colleges and Universities

Mechanical Engineering

Computational Biology

Electrical Engineering

Chemistry

Physics—Classical Mechanics

Developed by Frida Svensson, summer intern

Level: High schools

Learning Objectives

This collection of assignments treats classic mechanics for High School Students and Undergraduate Students.

The examples are playful and fun, without making the exercised easy at all.

Tricky formulas and advanced concepts become graspable with the help of SystemModeler, trough animation and diagrams.

The courseware is also suitable for students who are starting more advanced mechanics and need to repeat the basics.

Related Courses

This courseware has been adapted for High School and Undergraduate courses in Physics and Mechanics. Specific courses include:

Physics 1-3, Curriculum for Swedish Upper Secondary School — https://www.skolverket.se/publikationer?id=2975

Engineering Mechanics, Linköping University — http://kdb-5.liu.se/liu/lith/studiehandboken/enkursplan.lasso

Reading Material

Basic Physics, Karl F. Kuhn

Engineering Mechanics; Statics and Dynamics, E.W. Nelson, C.L. Best W.G. McLean

Fundamentals of Applied Dynamics, James H. Williams Jr

Physics—Classical Mechanics

The assignments

Bungee jump

This assignment sheet consists of a few exercises considering a Bungee Jump model and a free falling body.

The assignment will help the student understand physical phenomena such as force, oscillation, gravity and deceleration

How gravitation affects free falling bodies.

Exploring different parameters and initial values.

How the stiffness of a bungee jump cord will decelerate the body.

Observing frequency, amplitude and period time in a plot.

Bungee cord

In the first assignment the cord was approximated with a spring and a damper. In these assignments we look into the differences between this simplified model from earlier assignments and a set of more advanced models.

The assignment will help the students understand:

Models and theories as simplifications of reality.

The validity of models and theories and how they can be developed, generalized or replaced over time.

Trains

This assignment consists of a model of a train. The student will examine the couplings between the railway cars, and through this learn about force, deceleration, springs and dampers. The student is put in a realistic situation where the couplings need to be chosen according to safety, quality and price.

The assignment will help the students understand:

How springs and dampers can decelerate a body

Transitional mechanics and one dimensional collisions

Methodology for engineers and industrial problem solving.

Trampoline

This assignment sheet concerns a model of a trampoline and the different forces involved when jumping. The Assignment Sheet takes an approach of testing the trampoline for safety.

The assignment will help the students understand:

Engineering methodology and how to take safety measures based on mathematics.

To put classical physics in a context and give it a purpose

Free-body diagrams

Baseball

In this assignment we will study how we can manipulate the speed of a flying sphere to change it’s velocity by swinging a third class lever, or as some like to call it; baseball!

The assignment will help the students understand:

The difference between torque and force

Momentum and change of momentum in a collision

To calculate two-dimensional trajectories

Physics—Baseball

You can’t think & hit at the same time

The science that goes in to baseball is extremely complex and covers everything from impulse and momentum, to projectile trajectory, dynamic viscosity and torque. Let’s use a model to learn a bit of physics!

See https://www.youtube.com/watch?v=RENLMum5wz4

Learning Objectives

When this assignment has been completed, the students will have learned:

The difference between torque and force

Momentum and change of momentum in a collision

To calculate two-dimensional trajectories

Physics—Baseball

Let’s hit it!

Life Science—Population Genetics and Natural Selection

Developed by summer intern Anna Palmer.

Fundamental Concepts

Genetic inheritance

Evolutionary pressure

What is taught and why

Individual inheritance

Survival of the fittest (“Steady state solution”)

What we are asked to infer

How we move from individuals to populations

How it looks over time

How can we solve this discrepancy using system models?

Basic Population Model

The Model

Icons
The icons represent different stages in a human’s life:

 Birth

This is where a person’s life begins


Population Group

Represents the number of organisms within the population who have a particular trait. 

Death

This is where a person’s life ends.

Simulating the Model

Heterozygote Advantage

Malaria and Sickle Cell Anemia

Sickle cell anemia is a genetic disorder which affects red blood cells in the human body. People with sickle cell anemia have dysfunctional blood cells which ‘sickle’ (or form an odd shape) and break apart and die. This means that people with sickle cell anemia do not have enough red blood cells to support them. Although there have been advances in medical treatment, people with sickle cell anemia still have a reduced life span compared to people without the disease.

Malaria is an infectious disease, which is transmitted by mosquitoes. It is prevalent in South East Asia and African regions. After initially becoming infected with malaria (usually through a mosquito bite, from a mosquito infected with malaria), the parasite penetrates red blood cells making the person sick and sometimes, even causing death.

The Model

We assume that people with sickle cell anemia do not survive to reproduction, only people with the Healthy phenotype and people with the Carrier phenotype undergo reproduction in the model. Thus there are three different mating pairs that could possibly occur: a Healthy person mating with another Healthy person, a Healthy person mating with a Carrier, and a Carrier mating with a Carrier.

Simulating the Model

Targeting Highschool

Special consideration that need to be taken into account when considering highschool.

Manipulate elements

Hide advanced code

Auto load everything

Everything, including instructions and answer sheet, contained in single interactive notebook.

Chemistry

Developed by Emil Arkstål, summer intern

Laboratory Exercises

Step by step process. Follows a recipe (lap protocol)

Limited by the material costs.

Limited by the time actually performing the steps, waiting for machines.

Pellet and Supernatant

Discard the wrong one and you are done

Failing is an important part of learning

Red Blood Cell Isolation

Separate the hemoglobin from the plasma and the rest of the cell

Important for diagnosing sickle cell anaemia

Lot’s of steps, lot’s of mistakes to be made!

Hemoglobin Separation

Starting the exercise

The model has a set of starting values in a steady state. Two of these will be introduced here; the volume and NaCl concentration. Red blood cells are sensitive to changes in surrounding salt concentration. The solution used in the beginning of the lab (whole blood) is isotonic to the red blood cells, consisting of 0.9% NaCl.

1. Centrifugation

Keeping an eye on the volume and salt concentrations are important, but there would be no need if no dynamic interaction was not available. In order to remove the blood plasma but keep the red blood cells in the solution, we need to use a centrifuge, forcing the red blood cells into a pellet at the bottom the container the solution is in.

2. Remove Blood Plasma

Now that the red blood cells are gathered in the pellet, let’s remove the supernatant consisting of mostly blood plasma. In practice, this would generally be done using a single channel pipette. The red blood cells are covered in surface proteins, which we are not interested in. Therefore they must be washed using isotonic water.

3. Remove Surface Proteins

4. Hemolysis

5. Salting out Hemoglobin

6. Resolve Hemoglobin

7. Isolate Hemoglobin

Thanks!

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